Chapter 8. Experimental
Design II: Factorial Designs
Chapter 8. Experimental Design II: Factorial
Designs
Chapter Objectives
• Describe factorial designs using a standardized
notation system (2x2, 3x5, etc.) and place data
accurately into a factorial matrix to calculate row
and column means
• Understand what is meant by a main, interaction
effect and know how to determine if one exists
 Identify the varieties of factorials that correspond to the
single-factor designs of Chapter 7
Chapter Objectives
• Identify a mixed factorial design and a PxE factorial

Calculate the number of participants needed to complete
each type of factorial design

Construct an ANOVA source table for an independent
groups factorial design
Factorial Essentials
• Factorial design = more than one IV
• IVs referred to as “factors”
• Identifying factorial designs
• Notation system
• Digits represent IVs
• Numerical values of digits represent the # of levels of each IV
• 2x3 factorial (say: “two by three”)
• 2 IVs, one with 2 levels, one with 3 = 6 total conditions
• 2x4x4 factorial
• 3 IVs, with 2, 4, and 4 levels = 32 total conditions
Factorial Essentials
• Identifying factorial designs
• Factorial matrix
• 2x2 (two levels each of type of training and presentation rate)
Outcomes—Main Effects and Interactions
• Main Effects
• Overall effect of IV “type of training”
• Main effect compares data in both light-shaded cells (imagery)
with data in both dark-shaded cells (rote)
• Main effect compares row means (imagery vs. rote)
Outcomes—Main Effects and Interactions
• Main Effects
• Overall effect of IV “presentation rate”
• Main effect of compares data in both light-shaded cells (2-sec
rate) with data in both dark-shaded cells (4-sec rate)
• Main effect compares column means (2-sec vs. 4-sec)
Outcomes—Main Effects and Interactions
• Main Effects
• Calculations  row and
column means
• For hypothetical data:
• Row mean #1 (imagery) = 20
• Row mean #2
(rote) = 15
• Column mean #1
(2-sec) = 14.5
• Column mean #2
(4-sec) = 20.5
Outcomes—Main Effects and Interactions
• Main Effects
• For hypothetical data:
• Main effect for type of training
• Imagery (M = 20) produces better recall than rote (M = 15)
• Main effect for presentation rate
• 4-sec rate produces better recall (M = 20.5) than 2-sec rate (M = 14.5)
Outcomes—Main Effects and Interactions
• Interactions
• effect of one factor depends on the level of the other factor,
can be described two ways IVs  course emphasis and
student major
• No main effects (row and column means all equal 75)
Outcomes—Main Effects and Interactions
• Interactions
• Whether lab or lecture emphasis is better depends on which major
is being evaluated
• Lab emphasis  science majors do better (80>70)
• Lecture emphasis  humanities majors do better (80>70)
Outcomes—Main Effects and Interactions
• Interactions
• Whether science or humanities majors do better depends on what
type of course emphasis there is
• Science majors  better with lab emphasis (80>70)
• Humanities majors  better with lecture emphasis (80>70)
Outcomes—Main Effects and Interactions
• Interactions
• Research example 18: Studying in noise or silence
• IVs  study conditions (silent or noisy) and test conditions (silent
or noisy)
• No main effects, but an interaction
• Best memory when study and test conditions match
Outcomes—Main Effects and Interactions
• Interactions can trump main effects
• Caffeine, aging, and memory study
• Two main effects – neither relevant
Outcomes—Main Effects and Interactions
• Combinations of main effects and interactions
• Main effect for imagery instructions (22>14), no main effect
for presentation rate, no interaction
Outcomes—Main Effects and Interactions
• Combinations of main effects and interactions
• No main effect for imagery instructions, a main effect for
presentation rate (22>14), no interaction
Outcomes—Main Effects and Interactions
• Combinations of main effects and interactions
• Main effect for imagery instructions (20>16) and
presentation rate (20>16), no interaction
Outcomes—Main Effects and Interactions
• Combinations of main effects and interactions
• Interaction and two main effects
Outcomes—Main Effects and Interactions
• Combinations of main effects and interactions
• Interaction and two main effects
Outcomes—Main Effects and Interactions
• Combinations of main effects and interactions
• Line graphs occasionally used to highlight interactions
(nonparallel lines indicate interaction)
Varieties of Factorial Designs
Varieties of Factorial Designs
• Mixed factorial designs
• At least one IV is a between-subjects factor
• At least one IV is a within-subjects factor
Pre-Proactiv
New
Old
Post-Proactiv
12
4
14
11
Varieties of Factorial Designs
• Factorials with subject and manipulated variables : P
x E designs
• P = person factor (a subject variable)
• E = environmental factor (a manipulated variable)
• If E is a repeated measure  mixed P x E factorial
• Main effect for P factor
• Introverts outperform extroverts, regardless of room size
Varieties of Factorial Designs
• Factorials with subject and manipulated variables : P
x E designs
• Main effect for P factor
• Introverts outperform extroverts, regardless of room size
Varieties of Factorial Designs
• Factorials with subject and manipulated variables : P
x E designs
• Main effect for E factor
• Performance worse in small room, regardless of personality
Varieties of Factorial Designs
• Factorials with subject and manipulated variables : P
x E designs
• P x E interaction
• Introverts do better in large room, while extroverts do better in
small room
Summary
• Factorial designs allow us to evaluate the effects of multiple IVs on the
DV or DVs.
• There are different types of factorial designs, depending on how you
manipulate your IVs.
• Between-subjects, repeated measures, mixed, PxE
• Main effects of each IV and interactions among IVs are the results
from factorial designs.
• Factorial ANOVAs are the statistical tests used.
• With the experimental design tools at your disposal, remember to be
an ethical researcher.